Mathematics (Linear) 4365/1H

Transcription

1 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Pages Mark General Certificate of Secondary Education Higher Tier June 2014 Mathematics (Linear) 4365/1H Paper 1 H Monday 9 June am to am For this paper you must have: mathematical instruments. You must not use a calculator Time allowed 1 hour 30 minutes Instructions Use black ink or black ball-point pen. Draw diagrams in pencil. Fill in the es at the top of this page. Answer all questions. You must answer the questions in the spaces provided. around each page or on blank pages. Do all rough work in this book TOTAL Information The marks for questions are shown in brackets. The maximum mark for this paper is 70. The quality of your written communication is specifically assessed in Questions 2, 15 and 16. These questions are indicated with an asterisk (*). You may ask for more answer paper, tracing paper and graph paper. These must be tagged securely to this answer book. Advice In all calculations, show clearly how you work out your answer. (JUN H01) /E6w 4365/1H

2 2 Formulae Sheet: Higher Tier a 1 Area of trapezium = (a + b)h 2 h b Volume of prism = area of cross section length crosssection length 4 3 Volume of sphere = πr 3 r Surface area of sphere = 4πr Volume of cone = πr 2 h Curved surface area of cone = πrl l r h In any triangle ABC 1 2 Area of triangle = ab sin C a b c Sine rule = = sin A sin B sin C A b c C a B Cosine rule a 2 = b 2 + c 2 2bc cos A The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a 0, are given by b ± (b 2 4ac) x = 2a (02)

3 3 Answer all questions in the spaces provided. 1 Circle the correct word to describe the following. 1 (a) 2x 7y [1 mark] Equation Expression Formula Identity 1 (b) P = 2l + 2w [1 mark] Equation Expression Formula Identity 1 (c) 8(x y) 8x 8y [1 mark] Equation Expression Formula Identity Turn over for the next question 3 Turn over (03)

4 4 *2 A shop is having a sale on DVDs and CDs. DVDs are sold at one price. CDs are sold at a different price. 2 DVDs and 1 CD cost 35 2 DVDs and 2 CDs cost 45 Martin has 50 Does he have enough to buy 1 DVD and 3 CDs? You must show your working. [5 marks] (04)

5 5 3 (a) Write down four different numbers that have a median of 5 and a range of 7. Put the numbers in order. [2 marks] Answer...,...,...,... 3 (b) The table shows the scores of 20 students in a test. Score Frequency Total 20 Work out the mean score. [3 marks] Answer Turn over (05)

6 6 4 (a) Work out the area of this parallelogram. 6 cm 5 cm Not drawn accurately 8 cm State the units of your answer. [3 marks] Answer... (06)

7 7 4 (b) Shaz is drawing quadrilaterals on a nine-point square grid by joining points. For example She says, If you draw a quadrilateral it will always have line or rotational symmetry. Draw a quadrilateral on the grid below to show that Shaz is wrong. Use the first two grids for practice and the bottom grid for your answer. [1 mark] Practice grids Answer grid 4 Turn over (07)

8 8 5 (a) Work out the Highest Common Factor (HCF) of 24 and 42 [2 marks] Answer... 5 (b) As a product of prime factors 36 = Write 48 as a product of prime factors. [2 marks] Answer... (08)

9 9 6 Here are four scatter diagrams. A B C D Choose a letter to complete these sentences. [2 marks] Scatter diagram... shows no correlation. Scatter diagram... shows positive correlation. Scatter diagram... shows strong negative correlation. 6 Turn over (09)

10 10 7 This semi-circle has a radius of 5 cm Not drawn accurately 5 cm Work out the perimeter of the semi-circle. Remember to include the base. Use the approximation π = 3.1 [3 marks] Answer... cm (10)

11 11 8 (a) Solve x 2 = 36 [2 marks] Answer... y + 1 y 2 8 (b) Solve + = [4 marks] y =... 9 Turn over (11)

12 12 9 (a) The graph shows the line y = ax + b Work out the values of a and b. [2 marks] y x Answer a =... b =... (12)

13 13 9 (b) Work out the value of y when x = 80 [2 marks] Answer... Turn over for the next question 4 Turn over (13)

14 14 10 The table shows data about the times for men and women in a race. Mean Interquartile range Men 34m 50s 6m 30s Women 40m 10s 4m 45s Use data from the table to make two comparisons between the performances of the men and women in the race. [2 marks] Comparison 1 Comparison 2 (14)

15 15 11 Paul travels from Rye to Eston at an average speed of 90 km/h He travels for T hours. Mary makes the same journey at an average speed of 70 km/h She travels for 1 hour longer than Paul. Work out the value of T [4 marks] Answer... hours Turn over for the next question 6 Turn over (15)

16 16 12 A and B are independent events. Fill in all eight missing probabilities in the diagram below. [4 marks] 1 st event 2 nd event Outcome Probability... B A, B 0.12 A Not B A, Not B B Not A, B Not A... Not B Not A, Not B... (16)

17 17 13 The sum of two numbers is 15. The difference of the same two numbers is 8. Use algebra to work out the numbers. Do not use trial and improvement. You must show your working. [4 marks] Answer... and... Turn over for the next question 8 Turn over (17)

18 18 14 The diagram shows two rectangles. 3x cm (6x 3) cm Not drawn accurately 2 cm (4x + 1) cm 14 (a) Show the shaded area, in cm 2, is given by 12x 2 9x + 6 [2 marks] 14 (b) The shaded area is 6 cm 2 Calculate the value of x. [3 marks] Answer... (18)

19 19 *15 ABCD and AEFG are identical squares. CD = EF = 10 cm Angle BAG = 45º D Not drawn accurately E A 10 cm 10 cm 45 C F B G Prove that triangles AGD and ABE are congruent. [4 marks] 9 Turn over (19)

20 20 16 (a) Show clearly that (x y)(x + y) x 2 y 2 [1 mark] *16 (b) B Not drawn accurately ( 3 1) cm A cm C You are given that sin 75º = 2 2 Show that the area of triangle ABC is 2 1 cm 2 2 [3 marks] (20)

21 21 17 A pyramid has a square base of side 10 cm a height of 30 cm 30 cm 10 cm It is cut horizontally at a height of 15 cm The top pyramid is removed to leave this frustum. 15 cm 10 cm You are given the formula Volume of pyramid = 1 area of base vertical height 3 Calculate the volume of the frustum. [3 marks] Answer... cm 3 7 Turn over (21)

22 22 18 The diagram shows a ball being thrown. It is thrown from a height h metres above level ground. It lands 7.5 metres from where it was thrown. Not drawn accurately h m 7.5 m The path of the ball can be modelled by the equation y = (2x 1 + 1)(2x 15) 15 The sketch shows the graph of the equation. y h O 7.5 x (22)

23 23 18 (a) Work out the value of h. You must show your working. [2 marks] Answer (b) Show that the maximum height reached by the ball is 4 4 metres. 15 Use the symmetry of the graph to help you. You must show your working. [2 marks] END OF QUESTIONS 4 (23)

24 24 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Copyright 2014 AQA and its licensors. All rights reserved. (24)